Predicting air damping of micromachined mechanical resonators is crucial in the design of high Q devices for various applications. In the past, most of the work focused on devices in which the rarefaction effects of air are not significant. For such cases, continuum theory with suitable boundary conditions (either non-slip or slip) is often adequate. In this work, we investigate the air damping on oscillating structures in the free-molecule regime in which classical continuum theory is no longer valid. Such a study is important for devices operated at a very low pressure or for those whose characteristic length is of the nanometer scale. First, a careful examination of the related previous theoretical studies has been conducted. Mistakes and limitations have been found and reported in this paper. Next, a molecular dynamics simulation code has been developed and used in predicting quality factors of an oscillating microbeam operated at low pressures. Simulation results have shown an excellent agreement with experimental data. Finally, we investigate the effects of the Stokes number and the gap to oscillation amplitude ratio on the energy dissipation and quality factor of the microbeam.